by Yousef Al-Helou, Jabeen Bhatti and Janelle Dumalaon, Special for USA TODAY

by Yousef Al-Helou, Jabeen Bhatti and Janelle Dumalaon, Special for USA TODAY

GAZA CITY - The Israeli military continued to pound Gaza militants in the second day of its ground operation Saturday, demolishing more than a dozen tunnels as the death toll in the 12-day-old conflict climbed to 342.

While the Israeli military has been able to greatly reduce Hamas' arsenal, the militant group remains active, managing to infiltrate Israel from Gaza via a tunnel Saturday, killing two Israeli soldiers and injuring several others in the process.

During the first 24 hours of its ground offensive in Gaza, Israel says it discovered 34 shafts leading into about a dozen tunnels that could be used to carry out attacks.

"We have struck hard on the two main strategic assets of Hamas: the rockets and these tunnels," said Israeli military spokesman Lt. Col. Peter Lerner.

The Israeli military said it has hit 2,350 targets in Gaza, including 1,100 rocket launchers. Militants have fired more than 1,600 rockets since July 8.

In northern Gaza, officials reported intensified Israeli airstrikes and shelling, raising the death toll from the 12-day offensive to at least 342 Palestinians, Gaza Health Ministry spokesman Ashraf al-Kidra said. In Israel, a 30-year-old man was killed near the southern city of Dimona by a Gaza rocket, marking the second Israeli civilian casualty.

Early Saturday, Israeli tank fire killed at least five members of the Al Zawaydi family at their home in Beit Lahiya, including two children. In a separate incident, tank shell fire killed three members of the Hamooda family in their home, among them two children.

In Gaza City, two boys and a 1-year-old infant neighbor were killed Friday evening following the break of the Ramadan fast. On Saturday, at least two of the bodies were carried by somber relatives during a funeral procession in Gaza City.

A neighbor described the damage to the home as a "world turned upside down."

"The blood is filling the place everywhere. Small kids, it's a shame, they're kids," Amer al-Jumaasi said.

Israel says it is going to great lengths to avoid civilian casualties and blames them on Hamas, accusing it of firing from within residential neighborhoods and using civilians as "human shields."

Despite the high death toll, Gaza militants remain defiant.

"The Palestinian people in the Gaza Strip will not surrender to the enemy and will not raise the white flag," Ziad Nakhala, a leader in the Islamic Jihad militant group, told a Palestinian radio station. "We are open to all possibilities as long as the enemy does not respond to the demands of the resistance."

In Gaza, businesses are shut. Residents are hoarding food and other essentials as supplies run dry.

"We struggle to buy food as all the shops are closed. And inside the house, we face shortage of water when the electricity is cut - we have to queue to use the toilet," said Abu Saeid Banna, 47, who is hosting 30 people in his small apartment.

Even worse is the uncertainty of where the next shell will hit, with some Gaza residents saying targets are picked haphazardly.

"This war is the most brutal we have experienced so far," said Saeed Nassar, 54, of Gaza City. "The random indiscriminate tank shelling is a war crime - they attack civilians in their homes, on the street, everywhere."

Analysts say the ground offensive may require a week or more to destroy tunnels and rocket launchers used by Hamas militants to attack Israel.

"To occupy this area it's a matter of one day," Retired Maj. Gen. Shlomo Brom, former director of the Strategic Planning Division of the General Staff of the Israel Defense Forces, said Friday, a day after Israeli troops launched the offensive. "Then it takes time to clear the area. Searching can take a week or two."

Meanwhile, diplomats were struggling to revive cease-fire efforts after an Egyptian proposal was rejected by the militant group earlier this week. Hamas - the Palestinian branch of the Muslim Brotherhood - said they weren't consulted on the proposal's terms and felt Egypt could not fairly broker a deal a year after ousting the Muslim Brotherhood's Mohammed Morsi as president.

Egyptian Foreign Minister Sameh Shukri on Saturday repeated a call for Israel and Hamas to adopt its proposal.

"This initiative still presents the chance for the two sides to cease fire, ending the bloodshed," he said. "It meets the needs of both sides. We will continue to propose it. We hope both sides accept it."

In another effort to stop the violence, the head of the United Nations, Ban Ki-moon, is traveling to Gaza on Saturday.

"The secretary-general is extremely concerned that this escalation will further increase the already appalling death toll among Gazan civilians," U.N. Undersecretary-General for Political Affairs Jeffrey Feltman told reporters.

A peace deal could not come soon enough for many Gaza residents, who say the escalating situation is only creating more militants.

"Our children are traumatized," Banna said. "And when these children experience bad times, see dead bodies and blood, sound of explosions, this will change their personalities and you will hear the boys who lost (loved) ones say they want to join the resistance and avenge the death of their loved ones who were killed."